Two quotes from The Python 3.11.0 Language Reference (emphasize is mine):

• Note: If the object is a class instance and the attribute reference occurs on both sides of the assignment operator
• Delimiters: The second half of the list, the augmented assignment operators, serve lexically as delimiters, but also perform an operation

As explained at the expression entry term in the glossary, an operator is a syntatical element involved in an expression. An expression has a value. The piece of syntax (a = expr) is not an expression because it cannot be evaluated. And as explained at the same entry, assignment are also statement, not expression.

In the same way there is no del/return operator, it is not correct to invoke an assignment operator, the correct wording being "assignment statement" as used in many places in The Python Language Reference Manual. The only "assignment operator" we can figure out is the walrus operator because (a := expr) has a value.

For consistency, we can observe that assignment symbols (=, +=, etc), contrary to the walrus symbol, are not listed in:

• the set of tokens considered as operators
• the operator precedence table.

Thomas Wouters explains in a SO comment :

Assignment is actually not an expression in Python, and = not an operator in the normal sense; operator precedence doesn't apply.

Related reference of interest: = is not an operator

EDIT:

• Alex Martelli agrees here:

...doesn't exist, since '=' is not an operator in Python (just like it isn't, say, in VB). But, OK, you mean "assignment".

• Another reference of interest: Is assignment an operator in Python?